What is the solution for y^{''}+16y^'+100y=0,y(0)=0,y^'(0)=0 ?

The solution for y^{''}+16y^'+100y=0,y(0)=0,y^'(0)=0 is y=0

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y^{''}+16y^'+100y=0,y(0)=0,y^'(0)=0

y^{^{''}} + 16 y^{^{'}} + 100 y = 0, y (0) = 0, y^{^{'}} (0) = 0

y = 0

Solution steps

y^{''} (t) + 16 y^{'} (t) + 100 y = 0

Solve linear ODE:

y = 0

y = 0

y^{^{''}} + (\frac{25}{6}) y^{^{'}} + 25 y = 0

\frac{d ^{2} y}{d t ^{2}} + 16 y = 0, y (0) = 10, y^{^{'}} (0) = 0

(D^{3} - 1) y = 0

28 y^{^{''}} + 17 y^{^{'}} - 3 y = 0

x^{^{''}} + 6 x^{^{'}} + 25 x = 0, x (0) = \frac{1}{2}, x^{^{'}} (0) = 0

What is the solution for y^{''}+16y^'+100y=0,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+16y^'+100y=0,y(0)=0,y^'(0)=0 is y=0